The number of the realizations taken in the ensemble, \(M\) , also plays a role
in the behavior of the SVD modes. As can be seen in Fig. REF 
the slope for the low mode
does not depend on the number of realizations in the ensemble \(M\)  and remains
\(\alpha =2.5\)  for all values of \(M\) . On the other hand, for the high modes the
slope varies from \(\alpha =0.85\)  at \(M=1000\)  to \(\alpha =1\)  for the largest
number of realizations \(M=8000\) , in line with the predictions
for the Wigner-Dyson statistics. Such behavior
has been previously seen in the study of the
generalized Rosenzweig-Porter where the scree plot of the SVD modes for
large \(k\)  (the GOE regime) also follow a slope of \(\alpha \sim 0.8\) 
[1]} for small values of \(M\) . This behavior was attributed
there to the fact that there \(M << P\) . This fits well with our current
results where as \(M\)  grows \(\alpha \)  is closer to one.
<FIGURE>